SD stuff working for PAM6 and MLSE is also calibrated
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silas (home)
@@ -1,125 +1,181 @@
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function [GMI,NGMI] = calc_ngmi(test_signal,reference_signal,options)
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% Silas implementation of (N)GMI calculation according to: J. Cho, L. Schmalen, und P. J. Winzer,
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% „Normalized Generalized Mutual Information as a Forward Error Correction Threshold for Probabilistically Shaped QAM“,
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% in 2017 European Conference on Optical Communication (ECOC), Sep. 2017, doi: 10.1109/ECOC.2017.8345872.
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% This implementation assumes the same normal distributed noise for each
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% channel (sigma2 is calculated once for the whole signal)
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% (N)GMI for AWGN, supports PAM2/4/8 (per-symbol) and PAM6 (pair-based, 5 bits / 2 symbols)
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arguments(Input)
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test_signal;
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reference_signal;
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options.skip_front = 0;
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options.skip_end = 0;
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options.returnErrorLocation = 0;
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test_signal
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reference_signal
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options.skip_front (1,1) double = 0
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options.skip_end (1,1) double = 0
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options.returnErrorLocation (1,1) double = 0 %#ok<NASGU>
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end
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options.skip_end = abs(options.skip_end);
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options.skip_end = abs(options.skip_end);
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options.skip_front = abs(options.skip_front);
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assert((options.skip_end+options.skip_front) < numel(test_signal), ...
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"You can not skip more samples than the overall length.");
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assert((options.skip_end+options.skip_front)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
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if isa(reference_signal,'Signal'), reference_signal = reference_signal.signal; end
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if isa(test_signal,'Signal'), test_signal = test_signal.signal; end
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if isa(reference_signal,'Signal')
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reference_signal = reference_signal.signal;
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end
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% --- Trim head/tail consistently
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[test_signal,reference_signal] = trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
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if isa(test_signal,'Signal')
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test_signal = test_signal.signal;
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end
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% --- Noise variance (real AWGN): use mean-square error for robustness
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err = test_signal - reference_signal;
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sigma2 = mean((err(:)).^2);
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% TRIM
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[test_signal,reference_signal]=trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
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% --- Constellation (levels observed)
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constellation = unique(reference_signal);
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M = numel(constellation);
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% CALC EVM
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[GMI,NGMI] = calc_ngmi_(test_signal,reference_signal);
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% --- Empirical P_X (uniform is fine too; keep your original behavior)
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N = numel(reference_signal);
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counts = arrayfun(@(c) sum(reference_signal==c), constellation);
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P_X = counts / N;
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% --- Dispatch: PAM6 needs pairwise treatment (5 bits across 2 symbols)
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if M==6
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% ===== PAM6: 5 bits mapped to two consecutive symbols =====
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% Pair the sequence (drop last symbol if odd)
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numPairs = floor(N/2);
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if numPairs == 0
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GMI = 0; NGMI = 0; return;
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end
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y1 = test_signal(1:2:2*numPairs);
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y2 = test_signal(2:2:2*numPairs);
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x1 = reference_signal(1:2:2*numPairs);
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x2 = reference_signal(2:2:2*numPairs);
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function [GMI,NGMI] = calc_ngmi_(test_signal,reference_signal)
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% Build the 36 transition table and its 5-bit labels (ETH-style)
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symbols = sort(constellation); % keep fixed order
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% all pairs using ndgrid (no dependency on combvec)
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[S1,S2] = ndgrid(symbols, symbols); % MxM
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trans_pairs = [S1(:), S2(:)]; % (M^2) x 2
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assert(length(test_signal) == length(reference_signal),"Sequence length does not match");
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% Map those pairs to 5-bit labels using your PAMmapper (same as in your BCJR code)
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% NOTE: keep your normalization used by PAMmapper (sqrt(10)) if that's what it expects.
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bits72 = PAMmapper(6,0,"eth_style",0).demap( reshape(trans_pairs',[],1) );
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pam6bits = reshape(bits72', 5, []).'; % (M^2) x 5, row-aligned with trans_pairs
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%%% implemented according to [1] J. Cho, L. Schmalen, und P. J. Winzer,
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% „Normalized Generalized Mutual Information as a Forward Error Correction Threshold for Probabilistically Shaped QAM“,
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% in 2017 European Conference on Optical Communication (ECOC), Sep. 2017, S. 1–3. doi: 10.1109/ECOC.2017.8345872.
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% Precompute mapping (pair -> bit label) and (symbol -> index)
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[ok1, idx_s1] = ismember(trans_pairs(:,1), symbols);
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[ok2, idx_s2] = ismember(trans_pairs(:,2), symbols);
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assert(all(ok1)&all(ok2), 'Transition level not found in symbols.');
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% For fast masking: linear indices of each (i,j) pair in an MxM grid
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lin_idx_pairs = sub2ind([M,M], idx_s1, idx_s2); % (M^2) x 1
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error_vector = (test_signal-reference_signal);
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sigma2 = var(error_vector); %noise variance
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% Build pairwise prior P_pair = P_X(i)*P_X(j) on the MxM grid
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P_pair = P_X(:) * P_X(:).'; % MxM
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logP_pair = log(P_pair); % for numerical stability
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%%% Separate Classes
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constellation = unique(reference_signal);
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received_sd = NaN(numel(constellation),length(reference_signal));
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lvlcol = cbrewer2('Set1',numel(constellation));
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for lvl = 1:numel(constellation)
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%Separate the equalized signal into the
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%respective levels based on the actually
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%transmitted level!
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received_sd(lvl,reference_signal==constellation(lvl)) = test_signal(reference_signal==constellation(lvl));
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end
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% Precompute constant term for log-likelihood
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logc = -0.5*log(2*pi*sigma2);
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N = length(test_signal); % Number of received samples
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M = length(constellation); %P
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m = log2(M); %bits per symbol
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entries = sum(~isnan(received_sd),2)';
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P_X = ones(1,M)/M;%entries./N;
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% Parameters
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symbols = constellation'; % PAM-4 symbols
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gray_bits = PAMmapper(M,0).demap_(constellation); % Gray coding (bits per symbol)
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% Conditional probability function for AWGN
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q_Y_given_X = @(y, x) (1 / sqrt(2 * pi * sigma2)) * exp(-(y - x).^2 / (2 * sigma2));
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% Entropy term
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H_X = -sum(P_X .* log2(P_X)); % Entropy of input distribution
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tx_bits = PAMmapper(M,0,"eth_style",0).demap(reference_signal);
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% GMI computation
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bit_llr_sum = 0;
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for k = 1:N %loop over signal
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y_k = test_signal(k); % Current received sample
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% [~, closest_symbol_idx] = min(abs(symbols - y_k)); % Closest symbol index
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for i = 1:m %loop over bit position
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% Extract i-th bit for each symbol
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bit_mask = gray_bits(:, i); % Binary column for i-th bit of all symbols
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% matching_symbols = symbols(bit_mask == gray_bits(closest_symbol_idx, i)); %old, based on decision that mihht be wrong
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matching_symbols = symbols(bit_mask == tx_bits(k,i)); %new, based on tx bits
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% Numerator: Sum over x in x_{b_{k, i}}
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numerator = sum(q_Y_given_X(y_k, matching_symbols) .* P_X(ismember(symbols, matching_symbols)));
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% Denominator: Sum over all x
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denominator = sum(q_Y_given_X(y_k, symbols) .* P_X);
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% Logarithmic contribution
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bit_llr_sum = bit_llr_sum + log2(numerator / denominator);
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end
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end
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% Normalize the noise impact term by N
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bit_llr_sum = bit_llr_sum / N;
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% GMI
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GMI = H_X + bit_llr_sum;
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NGMI = GMI / m;
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% Prepare transmitted 5-bit labels per observed pair (to split llr0/llr1)
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% Find each (x1(k),x2(k)) in trans_pairs:
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[tf, row_in_table] = ismember([x1(:), x2(:)], trans_pairs, 'rows');
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assert(all(tf), 'A reference pair was not found in the transition table.');
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tx_bits_pair = pam6bits(row_in_table, :); % numPairs x 5
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% Precompute masks for bit=0 / bit=1 on the MxM grid for each bit position
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mask1 = false(M,M,5);
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mask0 = false(M,M,5);
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for b = 1:5
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tmp = false(M,M);
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tmp(lin_idx_pairs) = pam6bits(:,b) == 1;
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mask1(:,:,b) = tmp;
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tmp = false(M,M);
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tmp(lin_idx_pairs) = pam6bits(:,b) == 0;
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mask0(:,:,b) = tmp;
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end
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function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
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data_ = data(skipstart+1:end-skip_end,:);
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delta_bits = length(reference) - length(data);
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skip_end = delta_bits + skip_end;
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reference_ = reference(skipstart+1:end-skip_end,:);
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% Loop pairs: compute exact LLRs via log-sum-exp over the MxM grid
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LLR_exact = zeros(numPairs,5);
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for k = 1:numPairs
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% log-likelihood vectors along each axis
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li = logc - ((y1(k) - symbols).^2) / (2*sigma2); % 1xM
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lj = logc - ((y2(k) - symbols).^2) / (2*sigma2); % 1xM
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% joint log-weights over all (i,j)
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logW = (li(:) + lj(:).') + logP_pair; % MxM
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for b = 1:5
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% log P(bit=1 | y) ∝ logsumexp(logW over mask1)
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lnum = logsumexp(logW(mask1(:,:,b)));
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% log P(bit=0 | y) ∝ logsumexp(logW over mask0)
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lden = logsumexp(logW(mask0(:,:,b)));
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LLR_exact(k,b) = lnum - lden; % natural-log LLR
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end
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end
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end
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% --- Bitwise MI via consistency relation
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MI = zeros(1,5);
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for b = 1:5
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llr_b = LLR_exact(:,b);
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idx0 = (tx_bits_pair(:,b)==0);
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idx1 = ~idx0;
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I0 = mean( log2(1 + exp( llr_b(idx0))) ); % natural LLR inside exp()
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I1 = mean( log2(1 + exp(-llr_b(idx1))) );
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MI(b) = 1 - 0.5*(I0 + I1);
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end
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% GMI per symbol (5 bits per 2 symbols)
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GMI = sum(MI)/2;
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NGMI = GMI / 2.5;
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else
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% ===== Generic PAM2/4/8 etc.: per-symbol bit labeling =====
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symbols = constellation; % 1xM
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% Gray labels per symbol (your helper)
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gray_bits = PAMmapper(M,0).demap_(symbols); % M x log2(M)
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m = log2(M);
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% Likelihood (real AWGN)
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q = @(y,x) (1/sqrt(2*pi*sigma2)) * exp(-(y - x).^2/(2*sigma2));
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% Transmitted bits per sample
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tx_bits = PAMmapper(M,0,"eth_style",0).demap(reference_signal); % N x m
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% Exact bit-LLRs and MI
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LLR_exact = zeros(N,m);
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for b = 1:m
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mask1 = (gray_bits(:,b)==1);
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mask0 = ~mask1;
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for k = 1:N
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yk = test_signal(k);
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den = sum(q(yk, symbols) .* P_X);
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num1 = sum(q(yk, symbols(mask1)) .* P_X(mask1));
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num0 = sum(q(yk, symbols(mask0)) .* P_X(mask0));
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% Use the ratio of posteriors P(bit=1|y)/P(bit=0|y)
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LLR_exact(k,b) = log(num1) - log(num0); % natural log
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end
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end
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% Bitwise MI
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MI = zeros(1,m);
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for b = 1:m
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llr_b = LLR_exact(:,b);
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idx0 = (tx_bits(:,b)==0);
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idx1 = ~idx0;
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I0 = mean( log2(1 + exp( llr_b(idx0))) );
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I1 = mean( log2(1 + exp(-llr_b(idx1))) );
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MI(b) = 1 - 0.5*(I0 + I1);
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end
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% Per-symbol GMI/NGMI
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GMI = sum(MI);
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NGMI = GMI / m;
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end
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% ---------- helpers ----------
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function s = logsumexp(a)
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if isempty(a), s = -inf; return; end
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amax = max(a(:));
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s = amax + log(sum(exp(a(:) - amax)));
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end
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function [data_,reference_] = trimseq(data,reference,skipstart,skip_end)
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data_ = data(skipstart+1:end-skip_end,:);
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delta = numel(reference) - numel(data_);
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reference_ = reference(skipstart+1:end-(skip_end+delta),:);
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end
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end
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